OFFSET
1,3
COMMENTS
Conjecture: a(n) > 0 for all n > 1.
We have verified this for all n = 2..10^6.
Qing-Hu Hou at Tianjin University extended the verification to 2*10^7. Then I used Hou's program to verify a(n) > 0 for n up to 10^9. - Zhi-Wei Sun, May 28 2019
Conjecture verified for n up to 10^10. - Giovanni Resta, May 28 2019
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
Zhi-Wei Sun, On functions taking only prime values, J. Number Theory 133(2013), no.8, 2794-2812.
EXAMPLE
MATHEMATICA
f[n_]:=f[n]=FactorInteger[n];
FQ[n_]:=FQ[n]=n>0&&Part[f[n], Length[f[n]]][[1]]<4;
s[0]=0; s[n_]:=s[n]=Prime[n]-s[n-1];
tab={}; Do[r=0; Do[If[FQ[n-s[k]], r=r+1], {k, 1, 2n-1}]; tab=Append[tab, r], {n, 1, 100}]; Print[tab]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 25 2019
STATUS
approved